I would appreciate if you can solve this. Thank you.

A radio station in central Pennsylvania is having a birthday contest. One of the 366 days of the year is randomly selected with equal probability. If the month of a contestant's birthday matches the month selected - or the day of the month of the contestant's birthday matches the day of the month selected - or both - the contestant wins a compact disc. Otherwise, the contestant wins nothing. What is the probability that a contestant with a December 31 birthday will win? Express your answer as a common fraction.